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A 2.0 g bead slides along a frictionless wire,as shown in the figure.At point A,the bead is moving to the right but with negligible speed. A 2.0 g bead slides along a frictionless wire,as shown in the figure.At point A,the bead is moving to the right but with negligible speed. (a)What is the potential energy of the bead at point A? (b)What is the kinetic energy of the bead at point B? (c)What is the speed of the bead at point B? (d)What is the speed of the bead at point C? (a)What is the potential energy of the bead at point A? (b)What is the kinetic energy of the bead at point B? (c)What is the speed of the bead at point B? (d)What is the speed of the bead at point C?

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(a)2.0 × 1...

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When a particle is a distance r from the origin,its potential energy function is given by the equation When a particle is a distance r from the origin,its potential energy function is given by the equation ,where k is a constant and (a)What are the SI units of k? (b)Find a mathematical expression in terms of x,y,and z for the y component of the force on the particle. (c)If U = 3.00 J when the particle is 2.00 m from the origin,find the numerical value of the y component of the force on this particle when it is at the point (-1.00 m,2.00 m,3.00 m). ,where k is a constant and When a particle is a distance r from the origin,its potential energy function is given by the equation ,where k is a constant and (a)What are the SI units of k? (b)Find a mathematical expression in terms of x,y,and z for the y component of the force on the particle. (c)If U = 3.00 J when the particle is 2.00 m from the origin,find the numerical value of the y component of the force on this particle when it is at the point (-1.00 m,2.00 m,3.00 m). (a)What are the SI units of k? (b)Find a mathematical expression in terms of x,y,and z for the y component of the force on the particle. (c)If U = 3.00 J when the particle is 2.00 m from the origin,find the numerical value of the y component of the force on this particle when it is at the point (-1.00 m,2.00 m,3.00 m).

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(a)kg ∙ m/...

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In the figure,a very small toy race car of mass m is released from rest on the loop-the-loop track.If it is released at a height 2R above the floor,how high is it above the floor when it leaves the track,neglecting friction? In the figure,a very small toy race car of mass m is released from rest on the loop-the-loop track.If it is released at a height 2R above the floor,how high is it above the floor when it leaves the track,neglecting friction? A) 1.67 R B) 2.00 R C) 1.50 R D) 1.33 R E) 1.25 R


A) 1.67 R
B) 2.00 R
C) 1.50 R
D) 1.33 R
E) 1.25 R

F) B) and D)
G) A) and E)

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An athlete stretches a spring an extra 40.0 cm beyond its initial length.How much energy has he transferred to the spring,if the spring constant is 52.9 N/cm?


A) 423 J
B) 4230 kJ
C) 423 kJ
D) 4230 J

E) B) and D)
F) B) and C)

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A tennis ball bounces on the floor three times.If each time it loses 22.0% of its energy due to heating,how high does it rise after the third bounce,provided we released it A tennis ball bounces on the floor three times.If each time it loses 22.0% of its energy due to heating,how high does it rise after the third bounce,provided we released it from the floor? A) 110 cm B) 11 cm C) 110 mm D) 140 cm from the floor?


A) 110 cm
B) 11 cm
C) 110 mm
D) 140 cm

E) A) and D)
F) A) and C)

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A small hockey puck slides without friction over the icy hill shown in the figure and lands 6.20 m from the foot of the cliff with no air resistance.What was its speed v0 at the bottom of the hill? A small hockey puck slides without friction over the icy hill shown in the figure and lands 6.20 m from the foot of the cliff with no air resistance.What was its speed v<sub>0</sub> at the bottom of the hill? A) 20.8 m/s B) 17.4 m/s C) 14.4 m/s D) 13.7 m/s E) 4.71 m/s


A) 20.8 m/s
B) 17.4 m/s
C) 14.4 m/s
D) 13.7 m/s
E) 4.71 m/s

F) None of the above
G) B) and D)

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A box of mass m is pressed against (but is not attached to) an ideal spring of force constant k and negligible mass,compressing the spring a distance x.After it is released,the box slides up a frictionless incline as shown in the figure and eventually stops.If we repeat this experiment but instead compress the spring a distance of 2x A box of mass m is pressed against (but is not attached to) an ideal spring of force constant k and negligible mass,compressing the spring a distance x.After it is released,the box slides up a frictionless incline as shown in the figure and eventually stops.If we repeat this experiment but instead compress the spring a distance of 2x A) the box will go up the incline twice as high as before. B) just as it moves free of the spring, the box will be traveling twice as fast as before. C) just as it moves free of the spring, the box will be traveling four times as fast as before. D) just as it moves free of the spring, the box will have twice as much kinetic energy as before. E) just before it is released, the box has twice as much elastic potential energy as before.


A) the box will go up the incline twice as high as before.
B) just as it moves free of the spring, the box will be traveling twice as fast as before.
C) just as it moves free of the spring, the box will be traveling four times as fast as before.
D) just as it moves free of the spring, the box will have twice as much kinetic energy as before.
E) just before it is released, the box has twice as much elastic potential energy as before.

F) B) and D)
G) A) and D)

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A box of mass m is pressed against (but is not attached to) an ideal spring of force constant k and negligible mass,compressing the spring a distance x.After it is released,the box slides up a frictionless incline as shown in the figure and eventually stops.If we repeat this experiment with a box of mass 2m A box of mass m is pressed against (but is not attached to) an ideal spring of force constant k and negligible mass,compressing the spring a distance x.After it is released,the box slides up a frictionless incline as shown in the figure and eventually stops.If we repeat this experiment with a box of mass 2m A) the lighter box will go twice as high up the incline as the heavier box. B) just as it moves free of the spring, the lighter box will be moving twice as fast as the heavier box. C) both boxes will have the same speed just as they move free of the spring. D) both boxes will reach the same maximum height on the incline. E) just as it moves free of the spring, the heavier box will have twice as much kinetic energy as the lighter box.


A) the lighter box will go twice as high up the incline as the heavier box.
B) just as it moves free of the spring, the lighter box will be moving twice as fast as the heavier box.
C) both boxes will have the same speed just as they move free of the spring.
D) both boxes will reach the same maximum height on the incline.
E) just as it moves free of the spring, the heavier box will have twice as much kinetic energy as the lighter box.

F) B) and E)
G) D) and E)

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Is it possible for a system to have negative potential energy?


A) Yes, as long as the kinetic energy is positive.
B) Yes, as long as the total energy is positive.
C) Yes, since the choice of the zero of potential energy is arbitrary.
D) No, because the kinetic energy of a system must equal its potential energy.
E) No, because this would have no physical meaning.

F) A) and D)
G) A) and C)

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A potential energy function is given by U(x) = ( 3.00 N/m) x - ( 1.00 N/m3) x3.At what position or positions is the force equal to zero?


A) A potential energy function is given by U(x) = ( 3.00 N/m) x - ( 1.00 N/m<sup>3</sup>) x<sup>3</sup>.At what position or positions is the force equal to zero? A) m and - m B) 0.00 m, m and - m C) 1.00 m and -1.00 m D) 3.00 m and -3.00 m E) The force is not zero at any location. m and - A potential energy function is given by U(x) = ( 3.00 N/m) x - ( 1.00 N/m<sup>3</sup>) x<sup>3</sup>.At what position or positions is the force equal to zero? A) m and - m B) 0.00 m, m and - m C) 1.00 m and -1.00 m D) 3.00 m and -3.00 m E) The force is not zero at any location. m
B) 0.00 m, A potential energy function is given by U(x) = ( 3.00 N/m) x - ( 1.00 N/m<sup>3</sup>) x<sup>3</sup>.At what position or positions is the force equal to zero? A) m and - m B) 0.00 m, m and - m C) 1.00 m and -1.00 m D) 3.00 m and -3.00 m E) The force is not zero at any location. m and - A potential energy function is given by U(x) = ( 3.00 N/m) x - ( 1.00 N/m<sup>3</sup>) x<sup>3</sup>.At what position or positions is the force equal to zero? A) m and - m B) 0.00 m, m and - m C) 1.00 m and -1.00 m D) 3.00 m and -3.00 m E) The force is not zero at any location. m
C) 1.00 m and -1.00 m
D) 3.00 m and -3.00 m
E) The force is not zero at any location.

F) C) and D)
G) B) and E)

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A particle experiences a force given by A particle experiences a force given by .Find the potential field U(x) the particle is in.(Assume that the zero of potential energy is located at x = 0.) A) U(x) = -αx + x<sup>4</sup> B) U(x) = αx - x<sup>4</sup> C) U(x) = 3βx<sup>2</sup> D) U(x) = -3βx<sup>2</sup> .Find the potential field U(x) the particle is in.(Assume that the zero of potential energy is located at x = 0.)


A) U(x) = -αx + A particle experiences a force given by .Find the potential field U(x) the particle is in.(Assume that the zero of potential energy is located at x = 0.) A) U(x) = -αx + x<sup>4</sup> B) U(x) = αx - x<sup>4</sup> C) U(x) = 3βx<sup>2</sup> D) U(x) = -3βx<sup>2</sup> x4
B) U(x) = αx - A particle experiences a force given by .Find the potential field U(x) the particle is in.(Assume that the zero of potential energy is located at x = 0.) A) U(x) = -αx + x<sup>4</sup> B) U(x) = αx - x<sup>4</sup> C) U(x) = 3βx<sup>2</sup> D) U(x) = -3βx<sup>2</sup> x4
C) U(x) = 3βx2
D) U(x) = -3βx2

E) C) and D)
F) All of the above

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In the figure,a 4.0-kg ball is on the end of a 1.6-m rope that is fixed at 0.The ball is held at point A,with the rope horizontal,and is given an initial downward velocity.The ball moves through three quarters of a circle with no friction and arrives at B,with the rope barely under tension.The initial velocity of the ball,at point A,is closest to In the figure,a 4.0-kg ball is on the end of a 1.6-m rope that is fixed at 0.The ball is held at point A,with the rope horizontal,and is given an initial downward velocity.The ball moves through three quarters of a circle with no friction and arrives at B,with the rope barely under tension.The initial velocity of the ball,at point A,is closest to A) 4.0 m/s B) 5.6 m/s C) 6.3 m/s D) 6.9 m/s E) 7.9 m/s


A) 4.0 m/s
B) 5.6 m/s
C) 6.3 m/s
D) 6.9 m/s
E) 7.9 m/s

F) A) and B)
G) C) and E)

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Block 1 and block 2 have the same mass,m,and are released from the top of two inclined planes of the same height making 30° and 60° angles with the horizontal direction,respectively.If the coefficient of friction is the same in both cases,which of the blocks is going faster when it reaches the bottom of its respective incline?


A) We must know the actual masses of the blocks to answer.
B) Both blocks have the same speed at the bottom.
C) Block 1 is faster.
D) Block 2 is faster.
E) There is not enough information to answer the question because we do not know the value of the coefficient of kinetic friction.

F) A) and C)
G) A) and B)

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A 1.86-kg block is held in place against the spring by a 81-N horizontal external force (see the figure) .The external force is removed,and the block is projected with a velocity A 1.86-kg block is held in place against the spring by a 81-N horizontal external force (see the figure) .The external force is removed,and the block is projected with a velocity upon separation from the spring.The block descends a ramp and has a velocity at the bottom.The track is frictionless between points A and B.The block enters a rough section at B,extending to E.The coefficient of kinetic friction over this section is 0.28.The velocity of the block is v<sub>3</sub> = 1.4 m/s at C.The block moves on to D,where it stops.The height h of the ramp is closest to A) 11 B) 7.3 C) 15 D) 17 E) 18 upon separation from the spring.The block descends a ramp and has a velocity A 1.86-kg block is held in place against the spring by a 81-N horizontal external force (see the figure) .The external force is removed,and the block is projected with a velocity upon separation from the spring.The block descends a ramp and has a velocity at the bottom.The track is frictionless between points A and B.The block enters a rough section at B,extending to E.The coefficient of kinetic friction over this section is 0.28.The velocity of the block is v<sub>3</sub> = 1.4 m/s at C.The block moves on to D,where it stops.The height h of the ramp is closest to A) 11 B) 7.3 C) 15 D) 17 E) 18 at the bottom.The track is frictionless between points A and B.The block enters a rough section at B,extending to E.The coefficient of kinetic friction over this section is 0.28.The velocity of the block is v3 = 1.4 m/s at C.The block moves on to D,where it stops.The height h of the ramp is closest to A 1.86-kg block is held in place against the spring by a 81-N horizontal external force (see the figure) .The external force is removed,and the block is projected with a velocity upon separation from the spring.The block descends a ramp and has a velocity at the bottom.The track is frictionless between points A and B.The block enters a rough section at B,extending to E.The coefficient of kinetic friction over this section is 0.28.The velocity of the block is v<sub>3</sub> = 1.4 m/s at C.The block moves on to D,where it stops.The height h of the ramp is closest to A) 11 B) 7.3 C) 15 D) 17 E) 18


A) 11
B) 7.3
C) 15
D) 17
E) 18

F) A) and B)
G) A) and D)

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A 5.00-kg object moves clockwise around a 50.0 cm radius circular path.At one location,the speed of the object is 4.00 m/s.When the object next returns to this same location,the speed is 3.00 m/s. (a)How much work was done by nonconservative (dissipative)forces as the object moved once around the circle? (b)If the magnitude of the above nonconservative (dissipative)forces acting on the object is constant,what is the value of this magnitude?

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(a)-17.5 J...

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